compressed sensing and matrix completion
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
Nowadays we frequently encounter sensors generating high-dimensional data that make sampling by traditional ways difficult or even entirely impossible. Compressed sensing and matrix
completion are techniques where data is acquired at the data information rate rather than what would be expected by its ambient dimension.The main goal of the project is to extend these techniques to higher dimensions and heterogeneous data.
The first part of the project is concerned with sparse plus low rank models applied to hyperspectral imaging. Correlations in the hyperspectral images will be used to under-sample the tensor and then reconstruct it by optimising over the space of low tensor rank plus sparse innovations. We will consider a specific type of subsampling based on the use of mosaic filters. The aim is to understand what filter/image combination allow successful reconstruction, which could
potentially lead to practical methods for compressive multispectral imaging, which is also of interest to Selex ES.
The second part of the project will extend the aforementioned models to heterogeneous data types where disparate data of a common object is combined for reconstruction and/or classification.
This project falls within the EPSRC Numerical Analysis research area.
completion are techniques where data is acquired at the data information rate rather than what would be expected by its ambient dimension.The main goal of the project is to extend these techniques to higher dimensions and heterogeneous data.
The first part of the project is concerned with sparse plus low rank models applied to hyperspectral imaging. Correlations in the hyperspectral images will be used to under-sample the tensor and then reconstruct it by optimising over the space of low tensor rank plus sparse innovations. We will consider a specific type of subsampling based on the use of mosaic filters. The aim is to understand what filter/image combination allow successful reconstruction, which could
potentially lead to practical methods for compressive multispectral imaging, which is also of interest to Selex ES.
The second part of the project will extend the aforementioned models to heterogeneous data types where disparate data of a common object is combined for reconstruction and/or classification.
This project falls within the EPSRC Numerical Analysis research area.
People |
ORCID iD |
| Jared Tanner (Primary Supervisor) | |
| Simon Vary (Student) |
Publications
Tanner J
(2019)
Matrix Rigidity and the Ill-Posedness of Robust PCA and Matrix Completion
in SIAM Journal on Mathematics of Data Science
Vary S
(2021)
On low-rank plus sparse matrix sensing
Tanner J
(2020)
Compressed sensing of low-rank plus sparse matrices
Antonucci G
(2019)
Multispectral Snapshot Demosaicing Via Non-Convex Matrix Completion
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509310/1 | 01/10/2015 | 30/03/2021 | |||
| 1805810 | Studentship | EP/N509310/1 | 01/10/2016 | 31/03/2020 | Simon Vary |
| Description | We have applied matrix completion methods on a large dataset of multispectral images and observed that we can improve on the traditional interpolation methods by orders of magnitude. These could be potentially used for designing novel multispectral image cameras. We have also developed a theory and algorithms for guaranteed recovery of low-rank plus sparse matrix models. These can be used in multitude of contexts, including dynamic foreground / static background video separation and multispectral imaging. |
| Exploitation Route | Algorithms we have developed can be modified and possibly made practical in more specific applications. |
| Sectors | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software) |